An alternative explicit circuit diagram for the quantum search algorithm by implementing a non-unitary gate

• URL: http://arxiv.org/abs/2412.16514v4
• Date: Fri, 17 Jan 2025 06:58:52 GMT
• Title: An alternative explicit circuit diagram for the quantum search algorithm by implementing a non-unitary gate
• Authors: Ammar Daskin,
• Abstract summary: Since the final quantum state in the Grover search algorithm is the normalized marked quantum state in the Gram-Schmidt process, we can generate this vector by using a non-unitary gate. We present multiple explicit unitary implementations by using the square root of the non-unitary matrix and by a unitary matrix that mimics the Gram-Schmidt process.
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• Abstract: Since the final quantum state in the Grover search algorithm is the normalized marked quantum state in the Gram-Schmidt process, Abrams and Lloyd[1] has showed that we can generate this vector by using a non-unitary gate. Following their ideas, in this paper, we present multiple explicit unitary implementations by using the square root of the non-unitary matrix and by a unitary matrix that mimics the Gram-Schmidt process. We also discuss the implementation through a linear combination of unitary matrices or similar methods and how these approximations may change the complexity. The reading of the marked element from the given circuits with high probability still requires repetitions similar to the original algorithm. However, it gives an alternative implementations which may be useful in certain platforms

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